BPASBasePolynomial< Ring, Derived > Class Template Reference

An abstract class defining the interface of polynomial over an arbitrary BPASRing. More...

#include <BPASPolynomial.hpp>

Simplified semantic inheritance diagram for BPASBasePolynomial< Ring, Derived >:

 Full inheritance diagram for BPASBasePolynomial< Ring, Derived >:

Public Member Functions
virtual Derived &	operator= (const Ring &r)=0
	Assignment operator from the ground ring. More...
virtual Derived	operator+ (const Ring &r) const =0
	Addition operator of a ground ring element. More...
virtual Derived &	operator+= (const Ring &)=0
	Addition assignment operator of a ground ring element. More...
virtual Derived	operator- (const Ring &) const =0
	Subtraction operator of a ground ring element. More...
virtual Derived &	operator-= (const Ring &)=0
	Subtraction assignment operator of a ground ring element. More...
virtual Derived	operator- () const =0
	Negation operation. More...
virtual Derived	operator* (const Ring &) const =0
	Multiplication operator of a ground ring element. More...
virtual Derived &	operator*= (const Ring &)=0
	Multiplication assignment operator of a ground ring element. More...
virtual Integer	degree () const =0
	Return the (total) degree of polynomial. More...
virtual Ring	leadingCoefficient () const =0
	Get the leading coefficient of this polynomial, the non-zero coefficient of the monomial with maximum degree. More...
virtual Ring	trailingCoefficient () const =0
	Get the trailing coefficient of this polynomial, the non-zero coefficient of the monomial with minimum degree. More...
virtual bool	isConstantTermZero () const =0
	Determine if the constant term of this polynomial is zero or not. More...
virtual Integer	numberOfTerms () const =0
	Determine the number of non-zero terms in this polynomial. More...
Public Member Functions inherited from BPASRing< Derived >
virtual mpz_class	getCharacteristic () const
	The characteristic of this ring class.
virtual bool	isZero () const =0
	Determine if *this ring element is zero, that is the additive identity. More...
virtual void	zero ()=0
	Make *this ring element zero.
virtual bool	isOne () const =0
	Determine if *this ring element is one, that is the multiplication identity. More...
virtual void	one ()=0
	Make *this ring element one.
virtual Derived	unitCanonical (Derived *u=NULL, Derived *v=NULL) const =0
	Obtain the unit normal (a.k.a canonical associate) of an element. More...
virtual Derived &	operator= (const Derived &)=0
	Copy assignment.
virtual Derived	operator+ (const Derived &) const =0
	Addition.
virtual Derived &	operator+= (const Derived &)=0
	Addition assignment.
virtual Derived	operator- (const Derived &) const =0
	Subtraction.
virtual Derived &	operator-= (const Derived &)=0
	Subtraction assignment.
virtual Derived	operator* (const Derived &) const =0
	Multiplication.
virtual Derived &	operator*= (const Derived &)=0
	Multiplication assignment.
virtual Derived	operator^ (long long int e) const =0
	Exponentiation.
virtual Derived &	operator^= (long long int e)=0
	Exponentiation assignment.
virtual bool	operator== (const Derived &) const =0
	Equality test,. More...
virtual bool	operator!= (const Derived &) const =0
	Inequality test,. More...
virtual void	print (std::ostream &ostream) const
	Print the Ring element. More...
virtual std::string	toString () const
	Convert the Ring element to a string. More...
Public Member Functions inherited from ExpressionTreeConvert
virtual ExpressionTree	convertToExpressionTree () const =0
	Convert this to an expression tree. More...

Detailed Description

template<class Ring, class Derived>
class BPASBasePolynomial< Ring, Derived >

An abstract class defining the interface of polynomial over an arbitrary BPASRing.

This is class is the common interface for both univariate and multivariate polynomials.

Depending on the true type of Ring, the interface may add some additional methods.

See also

BPASEuclideanPolynomial, BPASGCDPolynomial, BPASIntegralPolynomial.

Since polynomials themselves form a ring, we inherit from BPASRing<Derived>, meanwhile the ground ring, Ring, must also be a valid ring.

Member Function Documentation

degree()

template<class Ring , class Derived >

virtual Integer BPASBasePolynomial< Ring, Derived >::degree ( ) const

pure virtual

Return the (total) degree of polynomial.

Returns

the degree.

isConstantTermZero()

template<class Ring , class Derived >

virtual bool BPASBasePolynomial< Ring, Derived >::isConstantTermZero ( ) const

pure virtual

Determine if the constant term of this polynomial is zero or not.

Returns

true iff the constant term is zero.

leadingCoefficient()

template<class Ring , class Derived >

virtual Ring BPASBasePolynomial< Ring, Derived >::leadingCoefficient ( ) const

pure virtual

Get the leading coefficient of this polynomial, the non-zero coefficient of the monomial with maximum degree.

Returns

the leading coefficient as a Ring.

numberOfTerms()

template<class Ring , class Derived >

virtual Integer BPASBasePolynomial< Ring, Derived >::numberOfTerms ( ) const

pure virtual

Determine the number of non-zero terms in this polynomial.

Returns

the number of terms.

operator*()

template<class Ring , class Derived >

virtual Derived BPASBasePolynomial< Ring, Derived >::operator* ( const Ring &  ) const

pure virtual

Multiplication operator of a ground ring element.

Parameters

r	a ground ring element to multiply.

Returns

the product.

operator*=()

template<class Ring , class Derived >

virtual Derived& BPASBasePolynomial< Ring, Derived >::operator*= ( const Ring &  )

pure virtual

Multiplication assignment operator of a ground ring element.

Parameters

r	a ground ring element to multiply.

Returns

a reference to this polynomial, updated after multiplicaiton.

operator+()

template<class Ring , class Derived >

virtual Derived BPASBasePolynomial< Ring, Derived >::operator+ ( const Ring &  r ) const

pure virtual

Addition operator of a ground ring element.

Parameters

r	a ground ring element to add.

Returns

the sum.

operator+=()

template<class Ring , class Derived >

virtual Derived& BPASBasePolynomial< Ring, Derived >::operator+= ( const Ring &  )

pure virtual

Addition assignment operator of a ground ring element.

Parameters

r	a ground ring element to add.

Returns

a reference to this polynomial, updated after addition.

operator-() [1/2]

template<class Ring , class Derived >

virtual Derived BPASBasePolynomial< Ring, Derived >::operator- ( const Ring &  ) const

pure virtual

Subtraction operator of a ground ring element.

Parameters

r	a ground ring element to subtract.

Returns

the difference.

operator-() [2/2]

template<class Ring , class Derived >

virtual Derived BPASBasePolynomial< Ring, Derived >::operator- ( ) const

pure virtual

Negation operation.

Obtain the additive inverse of this polynomial.

Returns

the negation of this polynomial.

Implements BPASRing< Derived >.

operator-=()

template<class Ring , class Derived >

virtual Derived& BPASBasePolynomial< Ring, Derived >::operator-= ( const Ring &  )

pure virtual

Subtraction assignment operator of a ground ring element.

Parameters

r	a ground ring element to subtract.

Returns

a reference to this polynomial, updated after subtraction.

operator=()

template<class Ring , class Derived >

virtual Derived& BPASBasePolynomial< Ring, Derived >::operator= ( const Ring &  r )

pure virtual

Assignment operator from the ground ring.

Parameters

r	a ground ring element to assign from.

Returns

a reference to this polynomial.

trailingCoefficient()

template<class Ring , class Derived >

virtual Ring BPASBasePolynomial< Ring, Derived >::trailingCoefficient ( ) const

pure virtual

Get the trailing coefficient of this polynomial, the non-zero coefficient of the monomial with minimum degree.

Returns

the trailing coefficient as a Ring.

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The documentation for this class was generated from the following file:

• include/Polynomial/BPASPolynomial.hpp